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Recent research in mobile robot navigation make it feasible to utilize autonomous robots in service fields. But, such applications require more than just navigation. To operate in a peopled environment, robots should recognize and act according to human social behavior. In this paper, we present the design and implementation of one such social behavior: a robot that stands in line much as people do. The system employs stereo vision to recognize lines of people, and uses the concept of personal space for modeling the social behavior. Personal space is used both to detect the end of a line and to determine how much space to leave between the robot and the person in front of it. Our model of personal space is based on measurements from people forming lines. We demonstrate our ideas with a mobile robot navigation system that can purchase a cup of coffee, even if people are waiting in line for service.